Two identical spheres are connected by an elastic tether. The tether obeys Hooke's Law for ideal springs. At a particular moment in time, the tether is in a straight line, at its resting length, neither stretching nor contracting. This assembly is then placed into a circular orbit around the Earth, and oriented so that a line drawn from one sphere through the tether and the other sphere points directly at the Earth.

Give a qualitative description of the motion of the two spheres relative to each other over time.

Being that the assembly is a small thing (one assumes), I'd imagine that the whole goes into some orbit eventually, with some rotation, placing on average a stretching of the tether, but with some contraction and expansion taking place.

As to what orbit, I wouldn't know. Maybe that's not part of the expected answer.